Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $4 \leq x \leq 5$?

Explanation:

Step1: Recall average rate of change formula

The average rate of change of $f(x)$ on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify $f(4)$ and $f(5)$ from the graph

From the graph, $f(4)=2$ and $f(5)=-2$.

Step3: Substitute values into the formula

$\text{Average rate of change} = \frac{f(5)-f(4)}{5-4} = \frac{-2 - 2}{5-4}$

Step4: Calculate the result

$\frac{-4}{1} = -4$

Answer:

$-4$